On the difference of Gaussian measure of two balls in Hilbert spaces

1989 ◽  
pp. 401-405 ◽  
Author(s):  
Tomasz Zak
Keyword(s):  
Hilbert Spaces ◽  
Gaussian Measure ◽  
Difference Of Gaussian ◽  
The Difference

scholarly journals Markerless Image Alignment Method for Pressure-Sensitive Paint Image

Sensors ◽  
2022 ◽  
Vol 22 (2) ◽  
pp. 453
Author(s):  
Kyosuke Suzuki ◽  
Tomoki Inoue ◽  
Takayuki Nagata ◽  
Miku Kasai ◽  
Taku Nonomura ◽  
...  
Keyword(s):  
Computational Cost ◽  
Measurement Data ◽  
Image Alignment ◽  
Feature Points ◽  
Alignment Method ◽  
Pressure Sensitive Paint ◽  
Pressure Sensitive ◽  
Difference Of Gaussian ◽  
Tracing Algorithm ◽  
The Difference

We propose a markerless image alignment method for pressure-sensitive paint measurement data replacing the time-consuming conventional alignment method in which the black markers are placed on the model and are detected manually. In the proposed method, feature points are detected by a boundary detection method, in which the PSP boundary is detected using the Moore-Neighbor tracing algorithm. The performance of the proposed method is compared with the conventional method based on black markers, the difference of Gaussian (DoG) detector, and the Hessian corner detector. The results by the proposed method and the DoG detector are equivalent to each other. On the other hand, the performances of the image alignment using the black marker and the Hessian corner detector are slightly worse compared with the DoG and the proposed method. The computational cost of the proposed method is half of that of the DoG method. The proposed method is a promising for the image alignment in the PSP application in the viewpoint of the alignment precision and computational cost.

scholarly journals The irreducibility of C*-algebras acting on Hilbert C*-modules

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2425-2433
Author(s):  
Runliang Jiang
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Compact Operators ◽  
C Algebra ◽  
C Algebras ◽  
The Difference

Let B be a C*-algebra, E be a Hilbert B module and L(E) be the set of adjointable operators on E. Let A be a non-zero C*-subalgebra of L(E). In this paper, some new kinds of irreducibilities of A acting on E are introduced, which are all the generalizations of those associated to Hilbert spaces. The difference between these irreducibilities are illustrated by a number of counterexamples. It is concluded that for a full Hilbert B-module, these irreducibilities are all equivalent if and only if the underlying C*-algebra B is isomorphic to the C*-algebra of all compact operators on a Hilbert space.

Approximate bandpass and frequency response models of the difference of Gaussian filter

2010 ◽  
Vol 283 (24) ◽  
pp. 4942-4948 ◽  
Author(s):  
Philip Birch ◽  
Bhargav Mitra ◽  
Nagachetan M. Bangalore ◽  
Saad Rehman ◽  
Rupert Young ◽  
...  
Keyword(s):  
Frequency Response ◽  
Gaussian Filter ◽  
Response Models ◽  
Difference Of Gaussian ◽  
The Difference

scholarly journals Schur complement preconditioners for multiple saddle point problems of block tridiagonal form with application to optimization problems

2018 ◽  
Vol 39 (3) ◽  
pp. 1328-1359 ◽  
Author(s):  
Jarle Sogn ◽  
Walter Zulehner
Keyword(s):  
Saddle Point ◽  
Hilbert Spaces ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Schur Complement ◽  
Saddle Point Problems ◽  
Schur Complements ◽  
The Difference ◽  
Optimality Systems ◽  
Tridiagonal Form

Abstract The importance of Schur-complement-based preconditioners is well established for classical saddle point problems in $\mathbb{R}^N \times \mathbb{R}^M$. In this paper we extend these results to multiple saddle point problems in Hilbert spaces $X_1\times X_2 \times \cdots \times X_n$. For such problems with a block tridiagonal Hessian and a well-defined sequence of associated Schur complements, sharp bounds for the condition number of the problem are derived, which do not depend on the involved operators. These bounds can be expressed in terms of the roots of the difference of two Chebyshev polynomials of the second kind. If applied to specific classes of optimal control problems the abstract analysis leads to new existence results as well as to the construction of efficient preconditioners for the associated discretized optimality systems.

STABILITY AND CONVERGENCE OF TWO-LEVEL DIFFERENCE SCHEMES IN INTEGRAL WITH RESPECT TO TIME NORMS

1998 ◽  
Vol 08 (06) ◽  
pp. 1055-1070 ◽  
Author(s):  
ALEXANDER A. SAMARSKII ◽  
PETR P. MATUS ◽  
PETR N. VABISHCHEVICH
Keyword(s):  
Hilbert Spaces ◽  
A Priori Estimates ◽  
A Priori ◽  
Mathematical Physics ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Priori Estimates ◽  
Linear Problems ◽  
The Difference ◽  
The Stability

Nowadays the general theory of operator-difference schemes with operators acting in Hilbert spaces has been created for investigating the stability of the difference schemes that approximate linear problems of mathematical physics. In most cases a priori estimates which are uniform with respect to the t norms are usually considered. In the investigation of accuracy for evolutionary problems, special attention should be given to estimation of the difference solution in grid analogs of integral with respect to the time norms. In this paper a priori estimates in such norms have been obtained for two-level operator-difference schemes. Use of that estimates is illustrated by convergence investigation for schemes with weights for parabolic equation with the solution belonging to [Formula: see text].

scholarly journals On a Polyanalytic Approach to Noncommutative de Branges–Rovnyak Spaces and Schur Analysis

2021 ◽  
Vol 93 (4) ◽  
Author(s):  
Daniel Alpay ◽  
Fabrizio Colombo ◽  
Kamal Diki ◽  
Irene Sabadini
Keyword(s):  
Hardy Space ◽  
Hilbert Spaces ◽  
Operator Theory ◽  
Schur Multipliers ◽  
Hyperholomorphic Functions ◽  
Polyanalytic Functions ◽  
Points Of View ◽  
The Difference ◽  
Space Case ◽  
Class Of Functions

AbstractIn this paper we begin the study of Schur analysis and of de Branges–Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that we consider the class of functions spanned by Appell-like polynomials. This approach is very efficient from various points of view, for example in operator theory, and allows us to make connections with the recently developed theory of slice polyanalytic functions. We tackle a number of problems: we describe a Hardy space, Schur multipliers and related results. We also discuss Blaschke functions, Herglotz multipliers and their associated kernels and Hilbert spaces. Finally, we consider the counterpart of the half-space case, and the corresponding Hardy space, Schur multipliers and Carathéodory multipliers.

scholarly journals Reverse inequalities for the numerical radius of linear operators in Hilbert spaces

2006 ◽  
Vol 73 (2) ◽  
pp. 255-262 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Linear Operator ◽  
Hilbert Spaces ◽  
Bounded Linear Operator ◽  
Upper Bounds ◽  
Linear Operators ◽  
Numerical Radius ◽  
Bounded Linear ◽  
The Difference ◽  
Reverse Inequalities

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

scholarly journals Optimization of the difference-of-Gaussian channel sets for the channelized Hotelling observer

2019 ◽  
Vol 6 (03) ◽  
pp. 1
Author(s):  
Christiana Balta ◽  
Ramona W. Bouwman ◽  
Mireille J. M. Broeders ◽  
Nico Karssemeijer ◽  
Wouter J. H. Veldkamp ◽  
...  
Keyword(s):  
Gaussian Channel ◽  
Hotelling Observer ◽  
Difference Of Gaussian ◽  
The Difference ◽  
Channelized Hotelling Observer

scholarly journals Small Infrared Target Detection via a Mexican-Hat Distribution

2019 ◽  
Vol 9 (24) ◽  
pp. 5570 ◽  
Author(s):  
Yubo Zhang ◽  
Liying Zheng ◽  
Yanbo Zhang
Keyword(s):  
Target Detection ◽  
Signal To Noise Ratio ◽  
Infrared Image ◽  
Small Target ◽  
Gaussian Filter ◽  
Adjacent Region ◽  
Detection Rates ◽  
Mexican Hat ◽  
Difference Of Gaussian ◽  
The Difference

Although infrared small target detection has been broadly used in airborne early warning, infrared guidance, surveillance and tracking, it is still an open issue due to the low signal-to-noise ratio, less texture information, background clutters, and so on. Aiming to detect a small target in an infrared image with complex background clutters, this paper carefully studies the characteristics of a target in an IR image filtered by the difference of Gaussian filter, concluding that the intensity of the adjacent region around a small infrared target roughly has a Mexican-hat distribution. Based on such a conclusion, a raw infrared image is sequentially processed with the modified top-hat transformation and the difference of Gaussian filter. Then, the adjacent region around each pixel in the processed image is radially divided into three sub-regions. Next, the pixels that distribute as the Mexican-hat are determined as the candidates of targets. Finally, a real small target is segmented out by locating the pixel with the maximum intensity. Our experimental results on both real-world and synthetic infrared images show that the proposed method is so effective in enhancing small targets that target detection gets very easy. Our method achieves true detection rates of 0.9900 and 0.9688 for sequence 1 and sequence 2, respectively, and the false detection rates of 0.0100 and 0 for those two sequences, which are superior over both conventional detectors and state-of-the-art detectors. Moreover, our method runs at 1.8527 and 0.8690 s per frame for sequence 1 and sequence 2, respectively, which is faster than RLCM, LIG, Max–Median, Max–Mean.

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